Properties

Label 588.4.k.d.521.7
Level $588$
Weight $4$
Character 588.521
Analytic conductor $34.693$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 2 x^{14} - 94 x^{12} - 128 x^{10} + 2719 x^{8} - 10368 x^{6} - 616734 x^{4} + 1062882 x^{2} + 43046721\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{12} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 521.7
Root \(1.34095 + 2.68363i\) of defining polynomial
Character \(\chi\) \(=\) 588.521
Dual form 588.4.k.d.509.7

$q$-expansion

\(f(q)\) \(=\) \(q+(4.64818 - 2.32260i) q^{3} +(3.31912 + 5.74888i) q^{5} +(16.2111 - 21.5917i) q^{9} +O(q^{10})\) \(q+(4.64818 - 2.32260i) q^{3} +(3.31912 + 5.74888i) q^{5} +(16.2111 - 21.5917i) q^{9} +(-37.9734 - 21.9239i) q^{11} +14.4990i q^{13} +(28.7802 + 19.0128i) q^{15} +(16.3257 - 28.2769i) q^{17} +(39.9956 - 23.0914i) q^{19} +(91.0734 - 52.5812i) q^{23} +(40.4669 - 70.0908i) q^{25} +(25.2033 - 138.014i) q^{27} -236.706i q^{29} +(-171.612 - 99.0804i) q^{31} +(-227.428 - 13.7096i) q^{33} +(140.121 + 242.696i) q^{37} +(33.6754 + 67.3940i) q^{39} +516.323 q^{41} -56.7471 q^{43} +(177.934 + 21.5304i) q^{45} +(14.8960 + 25.8006i) q^{47} +(10.2088 - 169.354i) q^{51} +(98.7936 + 57.0385i) q^{53} -291.073i q^{55} +(132.274 - 200.227i) q^{57} +(351.717 - 609.191i) q^{59} +(62.7826 - 36.2476i) q^{61} +(-83.3531 + 48.1239i) q^{65} +(-284.307 + 492.435i) q^{67} +(301.200 - 455.933i) q^{69} +1078.37i q^{71} +(-517.163 - 298.584i) q^{73} +(25.3049 - 419.783i) q^{75} +(-200.582 - 347.418i) q^{79} +(-203.401 - 700.049i) q^{81} +1117.48 q^{83} +216.747 q^{85} +(-549.773 - 1100.25i) q^{87} +(-35.1607 - 60.9001i) q^{89} +(-1027.81 - 61.9573i) q^{93} +(265.500 + 153.286i) q^{95} -1371.56i q^{97} +(-1088.97 + 464.498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{9} + O(q^{10}) \) \( 16 q + 12 q^{9} - 120 q^{15} - 320 q^{25} - 80 q^{37} + 732 q^{39} + 640 q^{43} - 552 q^{51} - 1560 q^{57} - 1840 q^{67} + 3176 q^{79} + 3456 q^{81} + 1920 q^{85} - 3960 q^{93} + 1152 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 4.64818 2.32260i 0.894542 0.446984i
\(4\) 0 0
\(5\) 3.31912 + 5.74888i 0.296871 + 0.514195i 0.975418 0.220361i \(-0.0707236\pi\)
−0.678548 + 0.734556i \(0.737390\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 16.2111 21.5917i 0.600411 0.799692i
\(10\) 0 0
\(11\) −37.9734 21.9239i −1.04086 0.600938i −0.120780 0.992679i \(-0.538540\pi\)
−0.920075 + 0.391741i \(0.871873\pi\)
\(12\) 0 0
\(13\) 14.4990i 0.309331i 0.987967 + 0.154666i \(0.0494300\pi\)
−0.987967 + 0.154666i \(0.950570\pi\)
\(14\) 0 0
\(15\) 28.7802 + 19.0128i 0.495400 + 0.327273i
\(16\) 0 0
\(17\) 16.3257 28.2769i 0.232915 0.403421i −0.725750 0.687959i \(-0.758507\pi\)
0.958665 + 0.284538i \(0.0918403\pi\)
\(18\) 0 0
\(19\) 39.9956 23.0914i 0.482927 0.278818i −0.238709 0.971091i \(-0.576724\pi\)
0.721635 + 0.692273i \(0.243391\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 91.0734 52.5812i 0.825657 0.476693i −0.0267064 0.999643i \(-0.508502\pi\)
0.852363 + 0.522950i \(0.175169\pi\)
\(24\) 0 0
\(25\) 40.4669 70.0908i 0.323735 0.560726i
\(26\) 0 0
\(27\) 25.2033 138.014i 0.179644 0.983732i
\(28\) 0 0
\(29\) 236.706i 1.51570i −0.652430 0.757849i \(-0.726250\pi\)
0.652430 0.757849i \(-0.273750\pi\)
\(30\) 0 0
\(31\) −171.612 99.0804i −0.994273 0.574044i −0.0877242 0.996145i \(-0.527959\pi\)
−0.906549 + 0.422101i \(0.861293\pi\)
\(32\) 0 0
\(33\) −227.428 13.7096i −1.19970 0.0723190i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 140.121 + 242.696i 0.622586 + 1.07835i 0.989002 + 0.147900i \(0.0472514\pi\)
−0.366416 + 0.930451i \(0.619415\pi\)
\(38\) 0 0
\(39\) 33.6754 + 67.3940i 0.138266 + 0.276710i
\(40\) 0 0
\(41\) 516.323 1.96673 0.983367 0.181631i \(-0.0581376\pi\)
0.983367 + 0.181631i \(0.0581376\pi\)
\(42\) 0 0
\(43\) −56.7471 −0.201252 −0.100626 0.994924i \(-0.532085\pi\)
−0.100626 + 0.994924i \(0.532085\pi\)
\(44\) 0 0
\(45\) 177.934 + 21.5304i 0.589442 + 0.0713235i
\(46\) 0 0
\(47\) 14.8960 + 25.8006i 0.0462298 + 0.0800724i 0.888214 0.459429i \(-0.151946\pi\)
−0.841985 + 0.539502i \(0.818613\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 10.2088 169.354i 0.0280298 0.464986i
\(52\) 0 0
\(53\) 98.7936 + 57.0385i 0.256044 + 0.147827i 0.622529 0.782597i \(-0.286105\pi\)
−0.366484 + 0.930424i \(0.619439\pi\)
\(54\) 0 0
\(55\) 291.073i 0.713604i
\(56\) 0 0
\(57\) 132.274 200.227i 0.307371 0.465275i
\(58\) 0 0
\(59\) 351.717 609.191i 0.776095 1.34424i −0.158082 0.987426i \(-0.550531\pi\)
0.934177 0.356810i \(-0.116136\pi\)
\(60\) 0 0
\(61\) 62.7826 36.2476i 0.131779 0.0760824i −0.432662 0.901556i \(-0.642425\pi\)
0.564440 + 0.825474i \(0.309092\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −83.3531 + 48.1239i −0.159057 + 0.0918314i
\(66\) 0 0
\(67\) −284.307 + 492.435i −0.518413 + 0.897918i 0.481358 + 0.876524i \(0.340144\pi\)
−0.999771 + 0.0213938i \(0.993190\pi\)
\(68\) 0 0
\(69\) 301.200 455.933i 0.525511 0.795477i
\(70\) 0 0
\(71\) 1078.37i 1.80252i 0.433281 + 0.901259i \(0.357356\pi\)
−0.433281 + 0.901259i \(0.642644\pi\)
\(72\) 0 0
\(73\) −517.163 298.584i −0.829169 0.478721i 0.0243993 0.999702i \(-0.492233\pi\)
−0.853568 + 0.520982i \(0.825566\pi\)
\(74\) 0 0
\(75\) 25.3049 419.783i 0.0389595 0.646298i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −200.582 347.418i −0.285661 0.494779i 0.687108 0.726555i \(-0.258880\pi\)
−0.972769 + 0.231776i \(0.925546\pi\)
\(80\) 0 0
\(81\) −203.401 700.049i −0.279013 0.960287i
\(82\) 0 0
\(83\) 1117.48 1.47783 0.738914 0.673800i \(-0.235339\pi\)
0.738914 + 0.673800i \(0.235339\pi\)
\(84\) 0 0
\(85\) 216.747 0.276583
\(86\) 0 0
\(87\) −549.773 1100.25i −0.677492 1.35586i
\(88\) 0 0
\(89\) −35.1607 60.9001i −0.0418767 0.0725325i 0.844327 0.535828i \(-0.180000\pi\)
−0.886204 + 0.463295i \(0.846667\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1027.81 61.9573i −1.14601 0.0690825i
\(94\) 0 0
\(95\) 265.500 + 153.286i 0.286734 + 0.165546i
\(96\) 0 0
\(97\) 1371.56i 1.43567i −0.696211 0.717837i \(-0.745132\pi\)
0.696211 0.717837i \(-0.254868\pi\)
\(98\) 0 0
\(99\) −1088.97 + 464.498i −1.10551 + 0.471553i
\(100\) 0 0
\(101\) 290.003 502.300i 0.285707 0.494858i −0.687074 0.726588i \(-0.741105\pi\)
0.972780 + 0.231729i \(0.0744384\pi\)
\(102\) 0 0
\(103\) −1342.66 + 775.185i −1.28443 + 0.741565i −0.977655 0.210217i \(-0.932583\pi\)
−0.306774 + 0.951782i \(0.599250\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1131.48 + 653.261i −1.02228 + 0.590216i −0.914765 0.403987i \(-0.867624\pi\)
−0.107520 + 0.994203i \(0.534291\pi\)
\(108\) 0 0
\(109\) −239.945 + 415.598i −0.210850 + 0.365202i −0.951981 0.306158i \(-0.900956\pi\)
0.741131 + 0.671360i \(0.234290\pi\)
\(110\) 0 0
\(111\) 1214.99 + 802.651i 1.03893 + 0.686344i
\(112\) 0 0
\(113\) 973.206i 0.810190i −0.914275 0.405095i \(-0.867238\pi\)
0.914275 0.405095i \(-0.132762\pi\)
\(114\) 0 0
\(115\) 604.566 + 349.046i 0.490227 + 0.283033i
\(116\) 0 0
\(117\) 313.058 + 235.045i 0.247370 + 0.185726i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 295.819 + 512.374i 0.222253 + 0.384954i
\(122\) 0 0
\(123\) 2399.96 1199.21i 1.75933 0.879098i
\(124\) 0 0
\(125\) 1367.04 0.978172
\(126\) 0 0
\(127\) 236.747 0.165417 0.0827083 0.996574i \(-0.473643\pi\)
0.0827083 + 0.996574i \(0.473643\pi\)
\(128\) 0 0
\(129\) −263.771 + 131.801i −0.180029 + 0.0899565i
\(130\) 0 0
\(131\) −813.694 1409.36i −0.542693 0.939971i −0.998748 0.0500200i \(-0.984071\pi\)
0.456055 0.889951i \(-0.349262\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 877.077 313.193i 0.559161 0.199669i
\(136\) 0 0
\(137\) −926.174 534.727i −0.577580 0.333466i 0.182591 0.983189i \(-0.441551\pi\)
−0.760171 + 0.649723i \(0.774885\pi\)
\(138\) 0 0
\(139\) 1854.85i 1.13184i −0.824459 0.565922i \(-0.808520\pi\)
0.824459 0.565922i \(-0.191480\pi\)
\(140\) 0 0
\(141\) 129.164 + 85.3284i 0.0771456 + 0.0509642i
\(142\) 0 0
\(143\) 317.876 550.577i 0.185889 0.321969i
\(144\) 0 0
\(145\) 1360.79 785.655i 0.779365 0.449966i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1586.85 916.167i 0.872481 0.503727i 0.00430915 0.999991i \(-0.498628\pi\)
0.868172 + 0.496264i \(0.165295\pi\)
\(150\) 0 0
\(151\) −1622.72 + 2810.64i −0.874539 + 1.51475i −0.0172860 + 0.999851i \(0.505503\pi\)
−0.857253 + 0.514895i \(0.827831\pi\)
\(152\) 0 0
\(153\) −345.888 810.898i −0.182767 0.428478i
\(154\) 0 0
\(155\) 1315.44i 0.681667i
\(156\) 0 0
\(157\) 46.0662 + 26.5963i 0.0234171 + 0.0135199i 0.511663 0.859186i \(-0.329030\pi\)
−0.488246 + 0.872706i \(0.662363\pi\)
\(158\) 0 0
\(159\) 591.688 + 35.6675i 0.295119 + 0.0177900i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1398.28 + 2421.90i 0.671915 + 1.16379i 0.977361 + 0.211581i \(0.0678611\pi\)
−0.305446 + 0.952209i \(0.598806\pi\)
\(164\) 0 0
\(165\) −676.044 1352.96i −0.318969 0.638349i
\(166\) 0 0
\(167\) −2577.35 −1.19426 −0.597131 0.802144i \(-0.703693\pi\)
−0.597131 + 0.802144i \(0.703693\pi\)
\(168\) 0 0
\(169\) 1986.78 0.904314
\(170\) 0 0
\(171\) 149.789 1237.91i 0.0669863 0.553598i
\(172\) 0 0
\(173\) 555.853 + 962.765i 0.244281 + 0.423108i 0.961929 0.273298i \(-0.0881146\pi\)
−0.717648 + 0.696406i \(0.754781\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 219.937 3648.52i 0.0933980 1.54938i
\(178\) 0 0
\(179\) 205.307 + 118.534i 0.0857285 + 0.0494954i 0.542251 0.840216i \(-0.317572\pi\)
−0.456523 + 0.889712i \(0.650905\pi\)
\(180\) 0 0
\(181\) 4627.46i 1.90031i 0.311775 + 0.950156i \(0.399077\pi\)
−0.311775 + 0.950156i \(0.600923\pi\)
\(182\) 0 0
\(183\) 207.636 314.304i 0.0838738 0.126962i
\(184\) 0 0
\(185\) −930.153 + 1611.07i −0.369655 + 0.640262i
\(186\) 0 0
\(187\) −1239.88 + 715.846i −0.484862 + 0.279935i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3333.31 1924.49i 1.26277 0.729063i 0.289164 0.957280i \(-0.406623\pi\)
0.973610 + 0.228217i \(0.0732894\pi\)
\(192\) 0 0
\(193\) −1013.30 + 1755.08i −0.377921 + 0.654578i −0.990760 0.135630i \(-0.956694\pi\)
0.612839 + 0.790208i \(0.290028\pi\)
\(194\) 0 0
\(195\) −275.668 + 417.284i −0.101236 + 0.153243i
\(196\) 0 0
\(197\) 606.043i 0.219182i 0.993977 + 0.109591i \(0.0349541\pi\)
−0.993977 + 0.109591i \(0.965046\pi\)
\(198\) 0 0
\(199\) −2526.72 1458.80i −0.900072 0.519657i −0.0228482 0.999739i \(-0.507273\pi\)
−0.877223 + 0.480082i \(0.840607\pi\)
\(200\) 0 0
\(201\) −177.784 + 2949.26i −0.0623877 + 1.03495i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1713.74 + 2968.28i 0.583866 + 1.01129i
\(206\) 0 0
\(207\) 341.083 2818.83i 0.114526 0.946483i
\(208\) 0 0
\(209\) −2025.02 −0.670209
\(210\) 0 0
\(211\) 117.626 0.0383779 0.0191890 0.999816i \(-0.493892\pi\)
0.0191890 + 0.999816i \(0.493892\pi\)
\(212\) 0 0
\(213\) 2504.61 + 5012.45i 0.805696 + 1.61243i
\(214\) 0 0
\(215\) −188.350 326.232i −0.0597459 0.103483i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3097.35 186.712i −0.955707 0.0576109i
\(220\) 0 0
\(221\) 409.987 + 236.706i 0.124791 + 0.0720479i
\(222\) 0 0
\(223\) 2306.55i 0.692636i 0.938117 + 0.346318i \(0.112568\pi\)
−0.938117 + 0.346318i \(0.887432\pi\)
\(224\) 0 0
\(225\) −857.364 2010.00i −0.254034 0.595555i
\(226\) 0 0
\(227\) −833.988 + 1444.51i −0.243849 + 0.422359i −0.961807 0.273727i \(-0.911743\pi\)
0.717958 + 0.696086i \(0.245077\pi\)
\(228\) 0 0
\(229\) 3061.60 1767.62i 0.883477 0.510076i 0.0116737 0.999932i \(-0.496284\pi\)
0.871803 + 0.489856i \(0.162951\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4921.10 + 2841.20i −1.38366 + 0.798855i −0.992590 0.121508i \(-0.961227\pi\)
−0.391066 + 0.920363i \(0.627894\pi\)
\(234\) 0 0
\(235\) −98.8830 + 171.270i −0.0274486 + 0.0475423i
\(236\) 0 0
\(237\) −1739.25 1148.99i −0.476694 0.314915i
\(238\) 0 0
\(239\) 1525.40i 0.412845i 0.978463 + 0.206422i \(0.0661821\pi\)
−0.978463 + 0.206422i \(0.933818\pi\)
\(240\) 0 0
\(241\) 4566.11 + 2636.25i 1.22045 + 0.704629i 0.965015 0.262196i \(-0.0844467\pi\)
0.255439 + 0.966825i \(0.417780\pi\)
\(242\) 0 0
\(243\) −2571.37 2781.54i −0.678822 0.734303i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 334.803 + 579.897i 0.0862471 + 0.149384i
\(248\) 0 0
\(249\) 5194.26 2595.46i 1.32198 0.660565i
\(250\) 0 0
\(251\) −5300.73 −1.33299 −0.666493 0.745512i \(-0.732205\pi\)
−0.666493 + 0.745512i \(0.732205\pi\)
\(252\) 0 0
\(253\) −4611.15 −1.14585
\(254\) 0 0
\(255\) 1007.48 503.416i 0.247415 0.123628i
\(256\) 0 0
\(257\) 1167.16 + 2021.58i 0.283290 + 0.490672i 0.972193 0.234181i \(-0.0752409\pi\)
−0.688903 + 0.724853i \(0.741908\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −5110.88 3837.27i −1.21209 0.910042i
\(262\) 0 0
\(263\) 1647.04 + 950.919i 0.386163 + 0.222951i 0.680496 0.732752i \(-0.261764\pi\)
−0.294333 + 0.955703i \(0.595098\pi\)
\(264\) 0 0
\(265\) 757.270i 0.175542i
\(266\) 0 0
\(267\) −304.879 201.410i −0.0698813 0.0461652i
\(268\) 0 0
\(269\) −3943.87 + 6830.99i −0.893911 + 1.54830i −0.0587651 + 0.998272i \(0.518716\pi\)
−0.835146 + 0.550028i \(0.814617\pi\)
\(270\) 0 0
\(271\) 3450.30 1992.03i 0.773398 0.446522i −0.0606872 0.998157i \(-0.519329\pi\)
0.834086 + 0.551635i \(0.185996\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3073.33 + 1774.39i −0.673924 + 0.389090i
\(276\) 0 0
\(277\) −2556.78 + 4428.47i −0.554592 + 0.960581i 0.443343 + 0.896352i \(0.353792\pi\)
−0.997935 + 0.0642293i \(0.979541\pi\)
\(278\) 0 0
\(279\) −4921.33 + 2099.19i −1.05603 + 0.450449i
\(280\) 0 0
\(281\) 3540.59i 0.751651i 0.926690 + 0.375825i \(0.122641\pi\)
−0.926690 + 0.375825i \(0.877359\pi\)
\(282\) 0 0
\(283\) 992.438 + 572.984i 0.208461 + 0.120355i 0.600596 0.799553i \(-0.294930\pi\)
−0.392135 + 0.919908i \(0.628263\pi\)
\(284\) 0 0
\(285\) 1590.11 + 95.8536i 0.330492 + 0.0199224i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1923.45 + 3331.51i 0.391501 + 0.678100i
\(290\) 0 0
\(291\) −3185.57 6375.24i −0.641723 1.28427i
\(292\) 0 0
\(293\) −573.089 −0.114267 −0.0571335 0.998367i \(-0.518196\pi\)
−0.0571335 + 0.998367i \(0.518196\pi\)
\(294\) 0 0
\(295\) 4669.55 0.921600
\(296\) 0 0
\(297\) −3982.86 + 4688.29i −0.778145 + 0.915968i
\(298\) 0 0
\(299\) 762.376 + 1320.47i 0.147456 + 0.255401i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 181.346 3008.34i 0.0343829 0.570378i
\(304\) 0 0
\(305\) 416.766 + 240.620i 0.0782424 + 0.0451733i
\(306\) 0 0
\(307\) 7901.69i 1.46897i 0.678626 + 0.734484i \(0.262576\pi\)
−0.678626 + 0.734484i \(0.737424\pi\)
\(308\) 0 0
\(309\) −4440.48 + 6721.65i −0.817508 + 1.23748i
\(310\) 0 0
\(311\) 4064.64 7040.16i 0.741108 1.28364i −0.210883 0.977511i \(-0.567634\pi\)
0.951991 0.306125i \(-0.0990326\pi\)
\(312\) 0 0
\(313\) −4554.84 + 2629.74i −0.822540 + 0.474893i −0.851291 0.524693i \(-0.824180\pi\)
0.0287519 + 0.999587i \(0.490847\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1284.32 741.501i 0.227553 0.131378i −0.381889 0.924208i \(-0.624727\pi\)
0.609443 + 0.792830i \(0.291393\pi\)
\(318\) 0 0
\(319\) −5189.53 + 8988.54i −0.910840 + 1.57762i
\(320\) 0 0
\(321\) −3742.06 + 5664.45i −0.650659 + 0.984918i
\(322\) 0 0
\(323\) 1507.93i 0.259764i
\(324\) 0 0
\(325\) 1016.25 + 586.731i 0.173450 + 0.100141i
\(326\) 0 0
\(327\) −150.044 + 2489.07i −0.0253744 + 0.420935i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1968.61 3409.73i −0.326902 0.566211i 0.654993 0.755635i \(-0.272671\pi\)
−0.981896 + 0.189423i \(0.939338\pi\)
\(332\) 0 0
\(333\) 7511.72 + 908.931i 1.23616 + 0.149577i
\(334\) 0 0
\(335\) −3774.60 −0.615607
\(336\) 0 0
\(337\) 6678.23 1.07948 0.539742 0.841830i \(-0.318522\pi\)
0.539742 + 0.841830i \(0.318522\pi\)
\(338\) 0 0
\(339\) −2260.36 4523.63i −0.362142 0.724749i
\(340\) 0 0
\(341\) 4344.47 + 7524.83i 0.689930 + 1.19499i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 3620.82 + 218.267i 0.565039 + 0.0340611i
\(346\) 0 0
\(347\) −6216.15 3588.90i −0.961673 0.555222i −0.0649851 0.997886i \(-0.520700\pi\)
−0.896687 + 0.442664i \(0.854033\pi\)
\(348\) 0 0
\(349\) 9025.65i 1.38433i −0.721738 0.692166i \(-0.756657\pi\)
0.721738 0.692166i \(-0.243343\pi\)
\(350\) 0 0
\(351\) 2001.06 + 365.424i 0.304299 + 0.0555694i
\(352\) 0 0
\(353\) −3884.78 + 6728.63i −0.585739 + 1.01453i 0.409044 + 0.912515i \(0.365862\pi\)
−0.994783 + 0.102015i \(0.967471\pi\)
\(354\) 0 0
\(355\) −6199.41 + 3579.23i −0.926846 + 0.535115i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3172.13 1831.43i 0.466347 0.269245i −0.248362 0.968667i \(-0.579892\pi\)
0.714709 + 0.699422i \(0.246559\pi\)
\(360\) 0 0
\(361\) −2363.07 + 4092.96i −0.344521 + 0.596728i
\(362\) 0 0
\(363\) 2565.06 + 1694.54i 0.370883 + 0.245014i
\(364\) 0 0
\(365\) 3964.14i 0.568473i
\(366\) 0 0
\(367\) 554.775 + 320.299i 0.0789073 + 0.0455572i 0.538935 0.842348i \(-0.318827\pi\)
−0.460027 + 0.887905i \(0.652160\pi\)
\(368\) 0 0
\(369\) 8370.16 11148.3i 1.18085 1.57278i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 3630.84 + 6288.81i 0.504016 + 0.872981i 0.999989 + 0.00464360i \(0.00147811\pi\)
−0.495973 + 0.868338i \(0.665189\pi\)
\(374\) 0 0
\(375\) 6354.23 3175.07i 0.875016 0.437227i
\(376\) 0 0
\(377\) 3432.01 0.468853
\(378\) 0 0
\(379\) −3738.41 −0.506674 −0.253337 0.967378i \(-0.581528\pi\)
−0.253337 + 0.967378i \(0.581528\pi\)
\(380\) 0 0
\(381\) 1100.44 549.868i 0.147972 0.0739385i
\(382\) 0 0
\(383\) −4953.94 8580.48i −0.660926 1.14476i −0.980373 0.197153i \(-0.936830\pi\)
0.319447 0.947604i \(-0.396503\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −919.933 + 1225.26i −0.120834 + 0.160940i
\(388\) 0 0
\(389\) 1814.06 + 1047.35i 0.236444 + 0.136511i 0.613541 0.789663i \(-0.289745\pi\)
−0.377098 + 0.926174i \(0.623078\pi\)
\(390\) 0 0
\(391\) 3433.69i 0.444116i
\(392\) 0 0
\(393\) −7055.56 4661.07i −0.905613 0.598269i
\(394\) 0 0
\(395\) 1331.51 2306.24i 0.169609 0.293771i
\(396\) 0 0
\(397\) 7406.31 4276.04i 0.936302 0.540574i 0.0475031 0.998871i \(-0.484874\pi\)
0.888799 + 0.458297i \(0.151540\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5260.04 3036.88i 0.655047 0.378191i −0.135340 0.990799i \(-0.543213\pi\)
0.790387 + 0.612608i \(0.209879\pi\)
\(402\) 0 0
\(403\) 1436.57 2488.21i 0.177570 0.307560i
\(404\) 0 0
\(405\) 3349.39 3492.87i 0.410944 0.428548i
\(406\) 0 0
\(407\) 12288.0i 1.49654i
\(408\) 0 0
\(409\) 10829.6 + 6252.49i 1.30927 + 0.755906i 0.981974 0.189016i \(-0.0605299\pi\)
0.327294 + 0.944923i \(0.393863\pi\)
\(410\) 0 0
\(411\) −5546.98 334.377i −0.665723 0.0401304i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 3709.06 + 6424.28i 0.438724 + 0.759892i
\(416\) 0 0
\(417\) −4308.07 8621.67i −0.505916 1.01248i
\(418\) 0 0
\(419\) 4950.15 0.577161 0.288581 0.957456i \(-0.406817\pi\)
0.288581 + 0.957456i \(0.406817\pi\)
\(420\) 0 0
\(421\) 7766.30 0.899065 0.449533 0.893264i \(-0.351591\pi\)
0.449533 + 0.893264i \(0.351591\pi\)
\(422\) 0 0
\(423\) 798.558 + 96.6269i 0.0917901 + 0.0111068i
\(424\) 0 0
\(425\) −1321.30 2288.56i −0.150806 0.261203i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 198.775 3297.48i 0.0223705 0.371104i
\(430\) 0 0
\(431\) 4585.49 + 2647.43i 0.512472 + 0.295876i 0.733849 0.679313i \(-0.237722\pi\)
−0.221377 + 0.975188i \(0.571055\pi\)
\(432\) 0 0
\(433\) 2694.81i 0.299086i −0.988755 0.149543i \(-0.952220\pi\)
0.988755 0.149543i \(-0.0477803\pi\)
\(434\) 0 0
\(435\) 4500.46 6812.44i 0.496047 0.750877i
\(436\) 0 0
\(437\) 2428.35 4206.03i 0.265821 0.460416i
\(438\) 0 0
\(439\) −5878.97 + 3394.23i −0.639153 + 0.369015i −0.784288 0.620397i \(-0.786972\pi\)
0.145135 + 0.989412i \(0.453638\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4231.11 + 2442.84i −0.453784 + 0.261992i −0.709427 0.704779i \(-0.751046\pi\)
0.255643 + 0.966771i \(0.417713\pi\)
\(444\) 0 0
\(445\) 233.405 404.269i 0.0248639 0.0430656i
\(446\) 0 0
\(447\) 5248.07 7944.11i 0.555313 0.840590i
\(448\) 0 0
\(449\) 9626.53i 1.01181i 0.862588 + 0.505907i \(0.168842\pi\)
−0.862588 + 0.505907i \(0.831158\pi\)
\(450\) 0 0
\(451\) −19606.5 11319.8i −2.04709 1.18189i
\(452\) 0 0
\(453\) −1014.73 + 16833.3i −0.105245 + 1.74591i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1526.92 2644.70i −0.156294 0.270708i 0.777236 0.629210i \(-0.216621\pi\)
−0.933529 + 0.358501i \(0.883288\pi\)
\(458\) 0 0
\(459\) −3491.14 2965.84i −0.355016 0.301598i
\(460\) 0 0
\(461\) 8767.63 0.885791 0.442895 0.896573i \(-0.353951\pi\)
0.442895 + 0.896573i \(0.353951\pi\)
\(462\) 0 0
\(463\) −10481.9 −1.05213 −0.526064 0.850445i \(-0.676333\pi\)
−0.526064 + 0.850445i \(0.676333\pi\)
\(464\) 0 0
\(465\) −3055.23 6114.38i −0.304694 0.609780i
\(466\) 0 0
\(467\) −1616.10 2799.17i −0.160138 0.277366i 0.774780 0.632231i \(-0.217860\pi\)
−0.934918 + 0.354864i \(0.884527\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 275.896 + 16.6313i 0.0269907 + 0.00162703i
\(472\) 0 0
\(473\) 2154.88 + 1244.12i 0.209475 + 0.120940i
\(474\) 0 0
\(475\) 3737.76i 0.361053i
\(476\) 0 0
\(477\) 2833.11 1208.46i 0.271948 0.115999i
\(478\) 0 0
\(479\) 5717.70 9903.35i 0.545404 0.944667i −0.453178 0.891420i \(-0.649710\pi\)
0.998581 0.0532469i \(-0.0169570\pi\)
\(480\) 0 0
\(481\) −3518.86 + 2031.61i −0.333568 + 0.192585i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7884.91 4552.35i 0.738217 0.426210i
\(486\) 0 0
\(487\) 3556.21 6159.54i 0.330898 0.573132i −0.651790 0.758399i \(-0.725982\pi\)
0.982688 + 0.185267i \(0.0593151\pi\)
\(488\) 0 0
\(489\) 12124.6 + 8009.77i 1.12125 + 0.740724i
\(490\) 0 0
\(491\) 11337.3i 1.04205i 0.853542 + 0.521025i \(0.174450\pi\)
−0.853542 + 0.521025i \(0.825550\pi\)
\(492\) 0 0
\(493\) −6693.31 3864.38i −0.611464 0.353029i
\(494\) 0 0
\(495\) −6284.74 4718.61i −0.570663 0.428456i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −5319.80 9214.16i −0.477248 0.826618i 0.522412 0.852693i \(-0.325032\pi\)
−0.999660 + 0.0260752i \(0.991699\pi\)
\(500\) 0 0
\(501\) −11980.0 + 5986.15i −1.06832 + 0.533816i
\(502\) 0 0
\(503\) 11859.2 1.05124 0.525621 0.850719i \(-0.323833\pi\)
0.525621 + 0.850719i \(0.323833\pi\)
\(504\) 0 0
\(505\) 3850.21 0.339272
\(506\) 0 0
\(507\) 9234.90 4614.48i 0.808947 0.404214i
\(508\) 0 0
\(509\) 753.362 + 1304.86i 0.0656035 + 0.113629i 0.896962 0.442109i \(-0.145769\pi\)
−0.831358 + 0.555737i \(0.812436\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2178.92 6101.92i −0.187527 0.525158i
\(514\) 0 0
\(515\) −8912.89 5145.86i −0.762619 0.440298i
\(516\) 0 0
\(517\) 1306.31i 0.111125i
\(518\) 0 0
\(519\) 4819.82 + 3184.08i 0.407642 + 0.269298i
\(520\) 0 0
\(521\) 1036.22 1794.78i 0.0871353 0.150923i −0.819164 0.573560i \(-0.805562\pi\)
0.906299 + 0.422637i \(0.138895\pi\)
\(522\) 0 0
\(523\) 12290.8 7096.08i 1.02761 0.593289i 0.111308 0.993786i \(-0.464496\pi\)
0.916298 + 0.400497i \(0.131163\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5603.37 + 3235.10i −0.463162 + 0.267407i
\(528\) 0 0
\(529\) −553.929 + 959.433i −0.0455271 + 0.0788553i
\(530\) 0 0
\(531\) −7451.74 17469.8i −0.608998 1.42773i
\(532\) 0 0
\(533\) 7486.18i 0.608372i
\(534\) 0 0
\(535\) −7511.04 4336.50i −0.606973 0.350436i
\(536\) 0 0
\(537\) 1229.61 + 74.1223i 0.0988114 + 0.00595645i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 3368.09 + 5833.71i 0.267663 + 0.463606i 0.968258 0.249953i \(-0.0804153\pi\)
−0.700595 + 0.713559i \(0.747082\pi\)
\(542\) 0 0
\(543\) 10747.7 + 21509.3i 0.849409 + 1.69991i
\(544\) 0 0
\(545\) −3185.63 −0.250380
\(546\) 0 0
\(547\) −2429.70 −0.189921 −0.0949604 0.995481i \(-0.530272\pi\)
−0.0949604 + 0.995481i \(0.530272\pi\)
\(548\) 0 0
\(549\) 235.130 1943.19i 0.0182789 0.151063i
\(550\) 0 0
\(551\) −5465.89 9467.19i −0.422604 0.731971i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −581.647 + 9648.92i −0.0444856 + 0.737971i
\(556\) 0 0
\(557\) −3223.03 1860.82i −0.245178 0.141554i 0.372376 0.928082i \(-0.378543\pi\)
−0.617554 + 0.786528i \(0.711876\pi\)
\(558\) 0 0
\(559\) 822.777i 0.0622536i
\(560\) 0 0
\(561\) −4100.57 + 6207.12i −0.308603 + 0.467139i
\(562\) 0 0
\(563\) 6433.94 11143.9i 0.481631 0.834209i −0.518147 0.855292i \(-0.673378\pi\)
0.999778 + 0.0210824i \(0.00671125\pi\)
\(564\) 0 0
\(565\) 5594.84 3230.18i 0.416596 0.240522i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −14068.6 + 8122.51i −1.03653 + 0.598442i −0.918849 0.394609i \(-0.870880\pi\)
−0.117683 + 0.993051i \(0.537547\pi\)
\(570\) 0 0
\(571\) 1046.20 1812.07i 0.0766761 0.132807i −0.825138 0.564931i \(-0.808903\pi\)
0.901814 + 0.432125i \(0.142236\pi\)
\(572\) 0 0
\(573\) 11024.0 16687.3i 0.803725 1.21662i
\(574\) 0 0
\(575\) 8511.20i 0.617290i
\(576\) 0 0
\(577\) 4200.54 + 2425.18i 0.303069 + 0.174977i 0.643821 0.765176i \(-0.277348\pi\)
−0.340752 + 0.940153i \(0.610682\pi\)
\(578\) 0 0
\(579\) −633.639 + 10511.4i −0.0454803 + 0.754472i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2501.02 4331.89i −0.177670 0.307733i
\(584\) 0 0
\(585\) −312.169 + 2579.88i −0.0220626 + 0.182333i
\(586\) 0 0
\(587\) 11785.0 0.828656 0.414328 0.910128i \(-0.364017\pi\)
0.414328 + 0.910128i \(0.364017\pi\)
\(588\) 0 0
\(589\) −9151.64 −0.640215
\(590\) 0 0
\(591\) 1407.59 + 2817.00i 0.0979707 + 0.196067i
\(592\) 0 0
\(593\) −3574.98 6192.05i −0.247566 0.428798i 0.715284 0.698834i \(-0.246298\pi\)
−0.962850 + 0.270037i \(0.912964\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −15132.8 912.222i −1.03743 0.0625373i
\(598\) 0 0
\(599\) 18893.6 + 10908.2i 1.28877 + 0.744071i 0.978435 0.206557i \(-0.0662259\pi\)
0.310334 + 0.950628i \(0.399559\pi\)
\(600\) 0 0
\(601\) 5591.30i 0.379490i −0.981833 0.189745i \(-0.939234\pi\)
0.981833 0.189745i \(-0.0607662\pi\)
\(602\) 0 0
\(603\) 6023.56 + 14121.6i 0.406796 + 0.953690i
\(604\) 0 0
\(605\) −1963.72 + 3401.26i −0.131961 + 0.228563i
\(606\) 0 0
\(607\) −2180.62 + 1258.98i −0.145813 + 0.0841852i −0.571132 0.820859i \(-0.693495\pi\)
0.425319 + 0.905044i \(0.360162\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −374.083 + 215.977i −0.0247689 + 0.0143003i
\(612\) 0 0
\(613\) 7826.27 13555.5i 0.515661 0.893151i −0.484174 0.874972i \(-0.660880\pi\)
0.999835 0.0181789i \(-0.00578683\pi\)
\(614\) 0 0
\(615\) 14859.9 + 9816.76i 0.974320 + 0.643659i
\(616\) 0 0
\(617\) 23431.7i 1.52889i −0.644688 0.764446i \(-0.723013\pi\)
0.644688 0.764446i \(-0.276987\pi\)
\(618\) 0 0
\(619\) 6719.35 + 3879.42i 0.436306 + 0.251901i 0.702030 0.712148i \(-0.252277\pi\)
−0.265723 + 0.964049i \(0.585611\pi\)
\(620\) 0 0
\(621\) −4961.58 13894.6i −0.320614 0.897860i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −521.012 902.419i −0.0333448 0.0577548i
\(626\) 0 0
\(627\) −9412.66 + 4703.31i −0.599530 + 0.299573i
\(628\) 0 0
\(629\) 9150.25 0.580039
\(630\) 0 0
\(631\) −18052.1 −1.13889 −0.569446 0.822029i \(-0.692842\pi\)
−0.569446 + 0.822029i \(0.692842\pi\)
\(632\) 0 0
\(633\) 546.749 273.199i 0.0343307 0.0171543i
\(634\) 0 0
\(635\) 785.791 + 1361.03i 0.0491074 + 0.0850564i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 23283.8 + 17481.5i 1.44146 + 1.08225i
\(640\) 0 0
\(641\) 4961.27 + 2864.39i 0.305707 + 0.176500i 0.645004 0.764179i \(-0.276856\pi\)
−0.339297 + 0.940679i \(0.610189\pi\)
\(642\) 0 0
\(643\) 707.722i 0.0434056i 0.999764 + 0.0217028i \(0.00690876\pi\)
−0.999764 + 0.0217028i \(0.993091\pi\)
\(644\) 0 0
\(645\) −1633.19 1078.92i −0.0997005 0.0658644i
\(646\) 0 0
\(647\) −4440.24 + 7690.72i −0.269805 + 0.467316i −0.968811 0.247799i \(-0.920293\pi\)
0.699006 + 0.715116i \(0.253626\pi\)
\(648\) 0 0
\(649\) −26711.7 + 15422.0i −1.61561 + 0.932770i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8576.46 + 4951.62i −0.513971 + 0.296741i −0.734464 0.678647i \(-0.762567\pi\)
0.220494 + 0.975388i \(0.429233\pi\)
\(654\) 0 0
\(655\) 5401.49 9355.65i 0.322219 0.558100i
\(656\) 0 0
\(657\) −14830.7 + 6326.03i −0.880671 + 0.375650i
\(658\) 0 0
\(659\) 25271.5i 1.49384i 0.664915 + 0.746919i \(0.268468\pi\)
−0.664915 + 0.746919i \(0.731532\pi\)
\(660\) 0 0
\(661\) −14626.1 8444.38i −0.860649 0.496896i 0.00358068 0.999994i \(-0.498860\pi\)
−0.864230 + 0.503098i \(0.832194\pi\)
\(662\) 0 0
\(663\) 2455.47 + 148.018i 0.143835 + 0.00867049i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −12446.3 21557.6i −0.722523 1.25145i
\(668\) 0 0
\(669\) 5357.18 + 10721.2i 0.309597 + 0.619592i
\(670\) 0 0
\(671\) −3178.76 −0.182883
\(672\) 0 0
\(673\) 17738.4 1.01600 0.507999 0.861358i \(-0.330385\pi\)
0.507999 + 0.861358i \(0.330385\pi\)
\(674\) 0 0
\(675\) −8653.59 7351.51i −0.493447 0.419200i
\(676\) 0 0
\(677\) 10421.1 + 18049.9i 0.591603 + 1.02469i 0.994017 + 0.109228i \(0.0348379\pi\)
−0.402414 + 0.915458i \(0.631829\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −521.512 + 8651.35i −0.0293457 + 0.486814i
\(682\) 0 0
\(683\) −21819.3 12597.4i −1.22239 0.705746i −0.256961 0.966422i \(-0.582721\pi\)
−0.965426 + 0.260676i \(0.916055\pi\)
\(684\) 0 0
\(685\) 7099.28i 0.395985i
\(686\) 0 0
\(687\) 10125.4 15327.0i 0.562312 0.851184i
\(688\) 0 0
\(689\) −827.003 + 1432.41i −0.0457276 + 0.0792025i
\(690\) 0 0
\(691\) 1405.33 811.366i 0.0773678 0.0446683i −0.460817 0.887495i \(-0.652444\pi\)
0.538185 + 0.842827i \(0.319110\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10663.3 6156.46i 0.581989 0.336011i
\(696\) 0 0
\(697\) 8429.31 14600.0i 0.458082 0.793421i
\(698\) 0 0
\(699\) −16275.2 + 24636.1i −0.880664 + 1.33308i
\(700\) 0 0
\(701\) 24658.8i 1.32860i −0.747466 0.664300i \(-0.768730\pi\)
0.747466 0.664300i \(-0.231270\pi\)
\(702\) 0 0
\(703\) 11208.4 + 6471.18i 0.601327 + 0.347176i
\(704\) 0 0
\(705\) −61.8338 + 1025.76i −0.00330326 + 0.0547977i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3438.97 5956.48i −0.182163 0.315515i 0.760454 0.649392i \(-0.224976\pi\)
−0.942617 + 0.333877i \(0.891643\pi\)
\(710\) 0 0
\(711\) −10753.0 1301.13i −0.567185 0.0686303i
\(712\) 0 0
\(713\) −20839.1 −1.09457
\(714\) 0 0
\(715\) 4220.27 0.220740
\(716\) 0 0
\(717\) 3542.89 + 7090.33i 0.184535 + 0.369307i
\(718\) 0 0
\(719\) 8473.37 + 14676.3i 0.439504 + 0.761243i 0.997651 0.0684988i \(-0.0218209\pi\)
−0.558147 + 0.829742i \(0.688488\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 27347.0 + 1648.51i 1.40670 + 0.0847976i
\(724\) 0 0
\(725\) −16590.9 9578.77i −0.849891 0.490685i
\(726\) 0 0
\(727\) 4172.21i 0.212845i 0.994321 + 0.106423i \(0.0339397\pi\)
−0.994321 + 0.106423i \(0.966060\pi\)
\(728\) 0 0
\(729\) −18412.6 6956.81i −0.935456 0.353443i
\(730\) 0 0
\(731\) −926.434 + 1604.63i −0.0468747 + 0.0811893i
\(732\) 0 0
\(733\) 26982.1 15578.1i 1.35963 0.784981i 0.370053 0.929011i \(-0.379339\pi\)
0.989573 + 0.144030i \(0.0460061\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21592.2 12466.3i 1.07919 0.623068i
\(738\) 0 0
\(739\) −4705.41 + 8150.01i −0.234224 + 0.405687i −0.959047 0.283248i \(-0.908588\pi\)
0.724823 + 0.688935i \(0.241921\pi\)
\(740\) 0 0
\(741\) 2903.09 + 1917.85i 0.143924 + 0.0950795i
\(742\) 0 0
\(743\) 26271.3i 1.29717i 0.761141 + 0.648586i \(0.224639\pi\)
−0.761141 + 0.648586i \(0.775361\pi\)
\(744\) 0 0
\(745\) 10533.9 + 6081.73i 0.518028 + 0.299084i
\(746\) 0 0
\(747\) 18115.6 24128.3i 0.887304 1.18181i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −9009.89 15605.6i −0.437784 0.758264i 0.559735 0.828672i \(-0.310903\pi\)
−0.997518 + 0.0704083i \(0.977570\pi\)
\(752\) 0 0
\(753\) −24638.7 + 12311.5i −1.19241 + 0.595823i
\(754\) 0 0
\(755\) −21544.0 −1.03850
\(756\) 0 0
\(757\) 15356.6 0.737314 0.368657 0.929565i \(-0.379818\pi\)
0.368657 + 0.929565i \(0.379818\pi\)
\(758\) 0 0
\(759\) −21433.5 + 10709.8i −1.02501 + 0.512177i
\(760\) 0 0
\(761\) −13195.0 22854.4i −0.628538 1.08866i −0.987845 0.155440i \(-0.950320\pi\)
0.359308 0.933219i \(-0.383013\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 3513.71 4679.93i 0.166063 0.221181i
\(766\) 0 0
\(767\) 8832.67 + 5099.55i 0.415814 + 0.240070i
\(768\) 0 0
\(769\) 12445.2i 0.583594i 0.956480 + 0.291797i \(0.0942531\pi\)
−0.956480 + 0.291797i \(0.905747\pi\)
\(770\) 0 0
\(771\) 10120.5 + 6685.82i 0.472737 + 0.312301i
\(772\) 0 0
\(773\) 691.097 1197.02i 0.0321566 0.0556968i −0.849499 0.527590i \(-0.823096\pi\)
0.881656 + 0.471893i \(0.156429\pi\)
\(774\) 0 0
\(775\) −13889.2 + 8018.96i −0.643763 + 0.371677i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 20650.6 11922.6i 0.949788 0.548361i
\(780\) 0 0
\(781\) 23642.1 40949.3i 1.08320 1.87616i
\(782\) 0 0
\(783\) −32668.7 5965.78i −1.49104 0.272286i
\(784\) 0 0
\(785\) 353.105i 0.0160546i
\(786\) 0 0
\(787\) 28319.4 + 16350.2i 1.28269 + 0.740561i 0.977339 0.211679i \(-0.0678930\pi\)
0.305351 + 0.952240i \(0.401226\pi\)
\(788\) 0 0
\(789\) 9864.34 + 594.632i 0.445095 + 0.0268308i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 525.554 + 910.286i 0.0235346 + 0.0407632i
\(794\) 0 0
\(795\) 1758.83 + 3519.92i 0.0784646 + 0.157030i
\(796\) 0 0
\(797\) −681.223 −0.0302762